Sharp inequalities for heat kernels of Schrodinger operators and applications to spectral gaps

This paper derives inequalities for multiple integrals from which sharp ine qualities for ratios of heat kernels and integrals of heat kernels of certa in Schrodinger operators follow. Such ratio inequalities imply sharp inequa lities for spectral gaps. The multiple integral inequalities, although very different, are motivated by the now classical Brascamp-Lieb Luttinger rear rangement inequalities. (C) 2000 Academic Press.